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9
Network Theorems
9.1 INTRODUCTION
This chapter will introduce the important fundamental theorems of network
analysis. Included are the superposition, Thévenin’s, Norton’s,
maximum power transfer, substitution, Millman’s, and reciprocity
theorems. We will consider a number of areas of application for each.
A thorough understanding of each theorem is important because a
number of the theorems will be applied repeatedly in the material to
follow.
9.2 SUPERPOSITION THEOREM
The superposition theorem, like the methods of the last chapter, can
be used to find the solution to networks with two or more sources that
are not in series or parallel. The most obvious advantage of this method
is that it does not require the use of a mathematical technique such as
determinants to find the required voltages or currents. Instead, each
source is treated independently, and the algebraic sum is found to determine
a particular unknown quantity of the network.
The superposition theorem states the following:
The current through, or voltage across, an element in a linear
bilateral network is equal to the algebraic sum of the currents or
voltages produced independently by each source.
When one is applying the theorem, it is possible to consider the
effects of two sources at the same time and reduce the number of networks
that have to be analyzed, but, in general,
Number of networks Number of
to be analyzed
� independent sources
(9.1)
To consider the effects of each source independently requires that
sources be removed and replaced without affecting the final result. To
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